Find AAA and BBB in 3x+1(x−1)(x+2)=Ax−1+Bx+2\dfrac{3x + 1}{(x-1)(x+2)} = \dfrac{A}{x-1} + \dfrac{B}{x+2}(x−1)(x+2)3x+1=x−1A+x+2B.
A=43, B=53A = \frac{4}{3},\ B = \frac{5}{3}A=34, B=35
A=53, B=−53A = \frac{5}{3},\ B = -\frac{5}{3}A=35, B=−35
A=43, B=13A = \frac{4}{3},\ B = \frac{1}{3}A=34, B=31
A=2, B=1A = 2,\ B = 1A=2, B=1